Experimental Investigation of Drag Reduction in Turbulent

Journal of Chemical and Petroleum Engineering 2021, 55(1): 117-137 DOI: 10.22059/jchpe.2021.307767.1323

RESEARCH PAPER

Experimental Investigation of Drag Reduction in

Turbulent Flow Using Biological and Synthetic

Macromolecules: A Comparative Study

Behrouz Raei*, Seyed Mohsen Peyghambarzadeh

Department of Chemical Engineering, Mahshahr Branch, Islamic Azad University, Mahshahr, Iran

Received: 07 August 2020, Revised: 08 January 2021, Accepted: 08 January 2021

© University of Tehran 2021

Abstract It was shown that the concept of drag-reducing in the pipe flow with the aid of

macromolecules is of great importance in practical engineering applications. In this

study, the drag-reducing the performance of three biological macromolecules

including guar gum (GG), xanthan gum (XG), and carboxymethyl cellulose (CMC)

was compared with three synthetic macromolecules including polyethylene oxide

(PEO), polyacrylamide (PAM), and polyacrylic acid (PAA). Results showed that

all the macromolecules enhanced the DR% except for GG. DR% for almost all of

the macromolecules deteriorated with increasing fluid flow rate. On the other hand,

DR% enhanced with increasing the pipe diameter for the synthetic polymers but

this effect is not obvious for biological polymeric solutions. Maximum DR was

44%, which occur at 1000 ppm concentration of XG at 30 °C and flow rate of 6

l/min and diameter ½ inch. Finally, a new correlation was developed for the

prediction of friction coefficient based on the Prandtl-Karman relation with the

newly adjusted slope which is a linear function of polymer concentration. This

correlation was in excellent agreement with the experimental data.

Keywords: Friction Coefficient,

Pipe,

Polymer,

Practical,

Solution

Introduction

High energy consumption and CO2 emissions are major concerns in the oil, gas,

petrochemical, and chemical process industries [1]. Drag reducing is one of the most effective

methods in this area. The concept of drag-reducing of pipe flow with drag-reducing agents

(DRAs) attracted the engineering applicable usages due to the ability of these agents to decrease

pumping power and increment the piping system capacity. Three categories are classified into

drag reduction additives: polymers, fibers, and surfactants. Drag reducing polymers (DRPs) are

long-chain with ultra-high molecular weight (usually 1 to 10 million) . For the first time, Toms

[2] reported in the 1940s that by adding long-chain polymers at low concentrations as a few

tenths ppm by weight, it is possible to reduce a great decrease in turbulent drag, up to 80%.

Despite many studies in this field, no explanation existed commonly accepted for the drag-

reducing mechanism [3-7]. Theories explaining the phenomenon of drag reduction are usually

classified into two classes in terms of the impacts of the polymer. Joseph et al.[8], De Gennes

[9] and Lumley [10] proposed some explanations in this regard. The elastic properties of

polymers were introduced by Joseph et al.[8] and De Gennes [9] as a reason for drag reduction.

Even in a very dilute mode, a polymer solution can be considered a viscoelastic fluid. Actually,

as a result of the capability of polymers storing elastic energy, shear waves can be propagated.

* Corresponding author:

Email: [email protected] (B. Raei)

118 Raei and Peyghambarzadeh

A normal cut-off fluctuate is provided by these shear waves at great frequencies. The cut-off

would then overwhelm the small eddies and probably result in a drag reduction. Lumley [10]

proposed the mechanism in terms of coiled polymer molecules elongation. The stretching of

coiled polymers increases the effective viscosity near the wall and thereby decreases the drag

by dampening the thickness of the viscous sub-layer and small vortices.

In experimental investigations on the impacts of polymers on turbulence, decreased

performance over time is complicated. Particularly, turbulence-related high shear systems can

result in thermal and mechanical degradation of drag-decreasing polymers [11].In these cases,

by breaking apart the polymer chains, known as scission, the drag-reducing impacts are

degraded [12]. In many practical applications, determining friction pressure losses of dilute

drag decreasing polymer solutions accurately is challenging. Virk et al.[13] demonstrated that

the friction factors of definite polymer solutions are much lower compared to the Newtonian

fluids. The reason is the polymer solution’s viscoelastic properties. In the turbulent flow zone,

the viscoelastic fluid’s friction factors are quite lower compared to Newtonian or pure viscous

fluids. The various polymer solutions' performance was examined by Virk [13] and discovered

a trend towards asymptotic maximum drag reduction in all cases.Numerous investigators

assessed the different drag affecting parameters. In the following section, drag reducer

macromolecules are reviewed separately.

Polyethylene Oxide (PEO)

Choi et al.[14] studied the impact of the concentration of the very dilute solution of

soluble PEO on turbulent DR in a rotating disk flow system. The findings showed that by

incrementing the PEO concentration to the maximum DR critical concentration, the DR

effectiveness of PEO was increased. DR performance decreased with a further rise in polymer

concentration. Kim et al.[15] used PEO as a potential drag-reducing in saltwater piping in an

ocean thermal energy conversion (OTEC) procedure and assessed the drag-reducing properties

and PEO mechanical degradation at different concentrations and molecular weights. The results

indicated that drag-reducing was primarily relied on time and persisted at the limit owing to

polymer chains degradation by degrading the polymer chains, drag reducing capacity decreased

considerably. The DR efficiency related to temperature was also studied. The findings showed

that, however, the percentage of the initial DR was maximum at room temperature where the

DR decreased fast. A greater DR effectiveness has been achieved at a lower temperature

compared to the higher temperature.

Choi et. al [16] assessed the efficiency of PEO drag reduction in synthetic seawater and

indicated that at a concentration of nearly 50 ppm for higher molecular weight PEO, a maximum

DR of 30% was achieved. Kim et al. [17] inspected the influences of the molecular weight and

concentration of the polyethylene oxides on the drag-reducing level through 4 concentrations

(1, 5, 10, and, 20 wppm) and 4 molecular weights of the polymer. They showed the maximum

drag-reducing rate of 50% at a concentration and molecular weight of 20 ppm and 4 × 106,

respectively. The drag-reducing impact also tends to increment by increasing the molecular

weight and the Reynolds number.

Polyacrylamide (PAM)

Sung et al.[18] assessed the DR effectiveness of PAM in a rotating disk flow system by co

mparing it with PEO. The temperature impact on DR was studied for both PAM and PEO at a

polymer concentration of 50 wppm. The findings indicated that the temperature increased the

mechanical degradation of the PEO chains, while PAM was stable mechanically even at high

temperatures. Therefore, for long-lasting transport usages and high temperatures, PAM is an

excellent DR additive in the future. The degradation phenomenon was also compared by

Journal of Chemical and Petroleum Engineering 2020, 55(1): 117-137 119

Sandoval et al. [19] with the use of a pipe flow device for 3 various aqueous solutions of PEO,

PAM, and Xanthan gum( XG). PEO and PAM possess flexible chains; however, the XG has a

rigid chain structure. The results showed that PAM was as effective as PEO, while the PAM

solution's DR efficiency was reduced to a lesser amount compared to PEO. In addition, the drag

reduction found by the rigid XG chain dropped shortly in the first stage and persisted constantly

different from the PEO and PAM instances. Zhang et al.[20] experimentally studied frictional

DR and heat transfer in the two-phase flow of air‐water with PAM additives and without it in a

horizontal circular tube. They indicated a decrease in the heat transfer coefficients by adding

PAM from 36.8% to 70.3% and the pressure drop from 31.9% to 54.7% in comparison to lack

of the PAM additive. Raei et al.[21] investigated the impact of PAM on heat transfer and

pressure drop in a double tube heat exchanger under turbulent flow. It was reported that the

DRA had an insignificant effect on the pressure drop; however, a reduction was shown in heat

transfer of about 25%. The influences of the addition of PAM to pure water in a compact heat

exchanger on pressure drop and heat transfer were experimentally investigated by

peyghambarzadeh et al.[22]. Results showed that the pressure drop continuously decreased by

adding PAM to water until concentrations of 100 ppm. The pressure drop started increasingly

after this optimum concentration. The maximum DR was 14%. In contrast, by increasing PAM

concentration, the total heat transfer coefficient was reduced. In this situation, the overall heat

transfer coefficient reduced by 28%.

Polyacrylic Acid (PAA)

Kim et al.[23] utilized a complex system of polymer-surfactants (PAA-SDS) as a drag-

reducing and assessed the impacts of pH and surfactant on the DR efficiency of PAA in an

exterior flow utilizing a rotating disk system. The findings showed that compared to the higher

pH, the DR efficiency at pH=4 was smaller representing the connection of the turbulent effects

of the polymers in water directly to their chains. They indicated that in a turbulent flow,

extending the conformation of PAA is more effective in drag-reducing in comparison to the

compact helical mode. In addition, increasing the SDS concentration (mol/L) intensified the

drag-reducing the effectiveness of PAA. Also, Kim et al. [24] investigated the conformational

variations of the PAA chains under highs shear flow and discovered a serious reduction in (DR

%) by incrementing the rotational speed of time and disk. They also stated that these drag-

reducing variations are sensitive to external factors like pH, molecular, and polymer weight of

PAA. Zhang et al. [25, 26] investigated the turbulent DR effectiveness of aqueous poly

(acrylamide- co-acrylic acid) copolymers within a rotating disk flow system with different

molecular parameters and indicated a highest DR of 45% at the concentration of 50 wppm.

Guar Gum (GG)

Kim et al. [27] investigated GG's DR behavior using a rotating disk device with 3 various

molecular weight fractions in water . They tested the efficiency of GG drag-reducing and found

that GG is an operative aqueous drag reducing agent and is more constant against mechanical

chain degradation compared to the synthetic aqueous drag-reducing components such as PEO.

The result showed that all the GG solutions increased the certain percentage drag decrease

within 62-80% of the primary DR efficiency. Deshmukh et al.[28] studied PAM grafting on

GG and compared the polymer of the graft with purified GG and commercial GG. They

discovered the good resistance of the purified GG and grafted GG to biodegradation and

increased efficiency of drag reduction. GG’s mechanical degradation is particularly assessed

by Hong et al. [29] in a turbulent flow where utilizing ultra-sonication 3 various molecular

weights of GG were prepared. A rotating disk system was used to calculate the efficiency of

the GG drag reduction as a function of time. They presented two various degradation models


of a single relaxation procedure and examined a stretched-exponential model, and it was found

that the stretched-exponential is well fitted to the investigational data. Eshghinejadfard et al.

[30] experimentally investigate the change in the pressure drop in a quasi-two-dimensional

channel flow utilizing different additives (including GG) considering two concentrations of 100

ppm and 300 ppm. Contrary to previous findings, GG showed no drag-reducing in Reynolds

numbers below 21,000. Within the low Reynolds range, an increased pressure drop was found

by both concentrations. The highest increment of 9.4% was found for 100 ppm GG solution. At

larger Reynolds numbers (Re>22,000), an obvious drag-reducing was observed.

Xanthan Gum (XG)

Sohn et al. [31] assessed the impact of different molecular factors on the DR of XG such as

polymer concentration, molecular weight, solution’s ionic strength, disk rotation speed, and

temperature. The results showed that a close relationship between the DR efficiency of XG and

different molecular parameters. Its greater shear stability in salt solutions and water was

documented in comparison with other flexible polymers. In the study of Hong et al. [32], the

effectiveness of DR caused by various concentrations of XG was investigated in aqueous KCl

solutions in a closed chamber through a rotating disk and it was indicated that mechanical

degradation decreased with increased KCl concentration as a function of time. The interaction

is allowed by anionic charges on XG allow between the added salt ions for inducing an XG

conformational variation in solution leading to the variations in the shear viscosity. The DR

improved at higher XG concentrations and the DR efficiency of XG/KCl decreased by

increasing KCl concentration because XG's polymeric chain conformation tends to be more

rigid, resulting in lower sensitivity to elevated shear conditions.

The drag-reducing effectiveness of PEO, PAM, and XG was analyzed by Andrade et al.

[33] through dissolving these 3 polymers with synthetic sea salt and without it in deionized

water. Utilizing a double-gap Couette-type rheometer tool, the impact of the salt concentration

was investigated on the DR over time. By the existence of salt, the highest DR efficiency for

both XG and PEO macromolecular solutions was reduced over time, though, not significant

change was found in the DR for PAM solutions. The sharp reduction in effectiveness is related

to the structural change from helical to the coil by adding salt.

To study the feasibility of enhancing the shear resistance of the hydrolyzed form of

polyacrylamide (HPAM), Habibpour et al. [34] prepared various PAM/XG and PAM/GG

mixtures and single GG and XG polymer solutions and measured the drag-reducing in a closed

flow loop. They indicated DR efficiency of both GG and XG solutions directly proportional to

polymer concentration and superior mechanical resistance was found in both solutions in

turbulent conditions. In dilute HPAM/XG solutions (C<300 wppm), the degree of DR was

decreased by adding XG and only shear stability was slightly enhanced. However, in

concentrated HPAM/XG solutions (C>450 wppm), with the XG concentration of over the

critical overlap concentration; both stability and DR efficiency were significantly enhanced by

adding XG.

Carboxy Methyl Cellulose (CMC)

Deshmukhet al. [35] presented a technique to synthesize CMC-based graft copolymers

through grafting acrylamide chains onto the CMC backbone while measuring their DR efficacy,

biodegradability, and shear stability. Results exhibited that the DR efficacy and decent

mechanical shear stability were improved by existing the grafted PAM chains, and it was also

found that these factors were reliant on the length and number of the grafts. Peyghambarzadeh

et al. [36] investigated the impacts of CMC in laminar flow using two types of CMC (CMC-Hi

molecular weight and CMC-Medium molecular weight) at different temperatures and


concentrations and measured the pressure drop and the heat transfer coefficient in an air-fined

heat exchanger. Their findings indicated that the drag-reducing percentage is increased by

incrementing temperature, DRA concentration, and fluid flow rate. It was also reported that by

incrementing DRA concentration, the overall heat transfer coefficient was continuously

decreased. In the study of Biswal and Singh [37], 6 various CMC-g-PAM copolymers were

synthesized by changing the quantity of catalyst and monomer, and significant viscosifying and

flocculation properties were found by these grafted copolymers.

In the present work, adding PAM, CMC, PEO, PAA, GG, and XG as DRAs into the water

during turbulent flow, inside circular smooth tubes was investigated. The impacts of various

factors on the pressure drop have been examined. The investigated factors in this research have

included been polymer type, polymer concentration, flow rate, temperature, and diameter of the

tubes. To have a comprehensive analysis of the results, the full factorial experiment was

conducted. Given the number of factors and levels, and, since all the tests have been repeated

at least three times, the total number of tests carried out in this study was over 1000.

Measurements and materials

Experimental setup

A schematic view of the experimental apparatus and a realistic photograph are shown

respectively in Figs. 1 and 2.

Fig. 1. Schematic of the experimental apparatus

Three concentrations of 6 kinds of dilute polymeric solutions as a drag reducer were

examined at three temperatures and flow rates in the device connected with two pipes, each

with a various diameter. Pipe No. 1 with a diameter of 0.0127 m is a rough pipe of carbon steel;

pipe No. 2 is made of carbon steel with a diameter of 0.01905 m. All pipes are 3 meters long.

For recycling the extra liquid to the tank, another pipe is also utilized. The tank is utilized as a

storing tank for the solution. The test loop includes one reservoir tank, digital thermostat

controller with PID controller, heater, centrifugal pumps, metal valves for closing and opening

the flow paths, flow meters, U-shaped manometer, and control box.


Fig. 2. Photograph of the experimental apparatus

The DRA solution is in a cylindrical 20 L carbon steel reservoir tank. At the bottom of the

tank, an electric heater is mounted with 6 kW of power that can heat the fluid to a boiling point.

A thermostat is joined to this heater to control the temperature with a digital display

(BR6FDMP4 models with a precision of ±0.1 °C) that shows and controls the temperature of

the tank. By obtaining the needed temperature, via a centrifugal pump (DELTA Company with

a maximum capacity of 50 L/min, 0.75 hp), the solution is pumped into the test section. It is

possible to adjust the fluid flow through a valve on the recycle line or a valve installed before

the flowmeter. The flow rate was measured using Rotameter (Technical Groups Model

sp.gr.1.0) with a 1.8–18 L/min flow rate. The accuracy of the flow meter is 0.1 L/min and was

calibrated by the time considered for a definite volume of discharging fluid. Utilizing a standard

manometer with an accuracy of 1 cm–H2O, the pressure drop was measured across the test

section.

Materials

To investigate the performance as the drag-reducing agent, 6 various water-soluble polymers

with high molecular weight were utilized. These polymers are commercially accessible

copolymers of polyethylene oxide (PEO), polyacrylamide (PAM), xanthan gum (XG),

polyacrylic acid (PAA), guar gum (GG), and carboxymethyl cellulose (CMC). The first three

polymers are classified as synthetic flexible molecules, however, the last three are regarded as

natural rigid polymer. The properties of drag reducer agents and the structures of six main

water-soluble polymers are summarized and are shown in Table 1.

Table 2 represents the working parameters ranges and the related uncertainties in measuring

them. The uncertainty in measuring the variables was calculated based on Moffat [38]. Also,

Table 3 shows the information of all the conducted tests.

Preparation

The polymer powders (PAM, CMC, PEO, and PAA) were weighed utilizing analytical

balance, with an accuracy of ±1 mg (Mettler Toledo XS603s). The polymer solutions were

prepared in a separate tank. At first, the polymer powders were dispersed progressively into the

deionized water and gradually stirred at 40 rpm to avoid agglutination of the particles on the

surface. For maintaining a constant rotating speed (rpm), the impeller’s speed was controlled

with a speed regulator. Each examination was performed after 24h, the time for completing

natural diffusion. This process was approved to prevent any polymer degradation before the

test initiation.


The GG solution was prepared using a mechanically stirred impeller with an intermediate

speed of almost 100 rpm. Using the low impeller speed, the separation of the polymer coils was

prevented before utilizing in experimental apparatus under turbulent flow. By adding the GG

in the vortex unceasingly at small intervals, the creation of aggregation was avoided in the

solution. The solution was stirred for 5 h and then left for hydration during the night.

Essentially, two homogenous and pseudo homogenous approaches exist for performing

drag-reducing tests utilizing XG [39]. However, through examinations, it was indicated that the

pseudo homogenous technique is more effective; therefore, it was utilized in the present study.

For obtaining concentrated stock polymer solutions, a suitable weight of polymer powder was

dissolved in deionized water. The solution was further gently magnetically agitated for 24 h till

complete dissolving. The solution was left unstirred for at least 12 h, so any structure produced

over stirring was relaxed and allowed to equilibrate.

Table 1. Specifications and structures of the employed polymers

Average

molecular

weight (g/mol)*

Supplier Type

Polymer Chemical Structure Name

2×106 Sigma-

Aldrich Synthetic

Polyethylene

oxide (PEO)

5 ×106 Sigma-

Aldrich Synthetic

Polyacrylamide

(PAM)

1.25×106 Sigma-

Aldrich Synthetic

Polyacrylic acid

(PAA)

1.08 ×106 Sigma-

Aldrich Biological

Guar Gum

(GG)

4.5 ×106 Sigma-

Aldrich Biological

Xanthan Gum

(XG)

15×106 Sigma-

Aldrich Biological

Carboxymethyl

cellulose

(CMC)

*Stated by manufacture


Table 2. The parameters and their uncertainty in this work Uncertainty Range Unit Quantity

±0.1 30-50 °C T (Temperature)

±0.1 6-10 l/min Q (Flow rate)

±0.05 12.7-19.05 mm D (Diameter)

±1% 0-1000 ppm C (Concentration)

±2.2% 8300-30000 - Re (Reynolds)

4.6% 195-2536 Pa ΔP (Pressure drop)

5.8% 0.02-0.13 - f (Friction factor)

Table 3. The information of the conducted experiments

` C (ppm) T (°C) Q (l/min) D (in)

PAA 100-200-360 30-40-50 6-8-10 1/2 -3/4

PEO 10-100-200 30-40-50 6-8-10 1/2 -3/4

XG 100-500-1000 30-40-50 6-8-10 1/2 -3/4

CMC 50-100-200 30-40-50 6-8-10 1/2 -3/4

PAM 10-100-200 30-40-50 6-8-10 1/2 -3/4

GG 10-250-500 30-40-50 6-8-10 1/2 -3/4

Data processing

A valid technique to examine the hydraulic impact of adding polymer to turbulent flow is to

measure the pressure drop (friction factor) and to compare the measured number against a base

state. For a definite flow rate, the Darcy friction factor is determined by [40]:

f =2D

ρu̅2(

ΔP

L) (1)

where, ΔP represents the pressure drop between a pair of pressure manometers located in the

test section and, L shows the distance between them. D denotes the diameter, is the solution

density, and �̅� shows its mean velocity over the test section.

The Reynolds number is determined normally as:

Re =ρu̅D

µP (2)

Here µ𝑝 shows the viscosity of the solution.

The effectiveness of the drag-reducing polymers is determined by the drag-reducing

percentage (DR%) in a flowing fluid normally stated quantitatively as follows. Hence, it is

possible to formulate the corresponding expressions in other dimensional mounts. The

percentage of drag-reducing (DR %) is explained as the relative difference between the friction

factor 𝑓𝑤of the solvent and 𝑓𝑝 , that of the polymeric solution, as:

DR% = (1 −fp

fw) × 100 (3)

It is also possible to represent the drag-reducing based on friction factor and Reynolds

number. In a more perceptive representation, the plot of these dimensionless amounts polymer

of solution based on Prandtl–Karman (P–K) parameters like 1

√𝑓 against 𝑅𝑒√𝑓 indicates that

over a certain Reynold number, the friction factor declines under that for only pure solvent flow.

There is a separate relationship between these parameters in Newtonian fluids for laminar and

turbulent regimes, similar to the polymer-solvent presented in Eqs. 4 and 5.


1

√f=

Re√f

16 Laminar flow (4)

1

√f= 4Log10(Re√f) − 0.4 Turbulent flow (5)

Eq. 6 provides the expression for Virk’s MDRA where the friction factor reaches an

asymptotic value.

1

√f= 19.0Log10(Re√f) − 32.4 (6)

Deionized water was used as a working fluid to examine the friction factor in the turbulent

flow regime to test the accuracy of the experimental apparatus. The experimental findings were

compared with the estimation of the Colebrook equation [40] as Eq. 7:

1

f12

= −2 × log (2.51

Ref12

+ε/D

3.7) (7)

where ε shows the roughness of the carbon steel tube equals 0.05 mm [40].

Dynamic rheological measurement

Viscosity is the most imperative property amongst the physical properties of the working

fluids with DRA since it is not possible to neglect its variation [3, 22, 36, 41]. In this work, the

SVM-3000 Anton Paar viscometer was used to measure the viscosity of various drag reducer

fluids. This device measures the kinematic and dynamic viscosity of fluid via only 2.5 ml of

the sample.

Results and discussion

Verification with pure water

First, the accuracy and reliability of the experimental apparatus were checked utilizing

distilled water as the working fluid. Through Eq. 1, friction factors (f) at various flow rates were

acquired, and the findings were compared with Eq. 7. An acceptable consistency was found

between the experimental data and the estimation of the Colebrook equation with an average

deviation of 10%. This little deviation can mainly be attributed to the not existence of accuracy

in calculating the minor losses caused by abrupt contractions and expansions.

The viscosity of polymeric fluids

In this work, the viscosity of the solutions including synthetic and biological polymers was

experimentally measured at various concentrations and 3 different temperatures of 30 °C, 40

°C, and 50 °C, and Fig. 3 represents the results. According to Fig. 3, by increasing the

concentration of the DRAs, the polymeric solutions viscosity increments too. However, the

slope of these changes is higher for XG, PAA, and GG polymers. Besides, the viscosity of the

solutions decreases with increasing temperature.


Fig. 3. The polymeric fluid viscosity as a function of concentrations and temperatures

(a) Synthetic DRA (b) Biological DRA

Drag reducing in polymeric solutions

Figs. 4 and 5 display the variation of DR% as a function of volume flow rate for two types

of polymeric solutions including synthetic and biological polymers at the temperature of 30 oC

inside the pipes with ½ and ¾ inches diameter. Results show that DR% improves when the

polymer concentration increases. This outcome is incomplete consensus with the results of

Mowla and Naderi [42], and Peyghambarzadeh et al [36]. But, with increasing GG

concentration, the amount of drugs has increased. It can probably due to the supererogatory

increase of viscosity of the solution with the addition of GG. Habibpour et al [34] reported that

GG has lower efficiency in drag-reducing comparing with XG and hydrolyzed PAM due to its

low molecular weight and low flexibility. The results of this study also represent that the flow

rate (or Re) effect on the drag-reducing is not uniform for different polymers. DR% decreases

with increasing flow rate for PAM, PEO, and XG while it does not change meaningfully for the

cases of CMC and PAA. Indeed, results revealed that increasing flow rate had more effect on

0

0.001

0.002

0.003

0.004

0.005

0 100 200 300 400

µ (

Pa

.s)

C (ppm)

PAA at T=30C

PAA at T=40C

PAA at T=50C

PAM at T=30C

PAM at T=40C

PAM at T=50C

PEO at T=30C

PEO at T=40C

PEO at T=50C

a

0.0004

0.0008

0.0012

0.0016

0.002

0 200 400 600 800 1000 1200

µ (

Pa

.s)

C (ppm)

CMC at T=30C

CMC at T=40C

CMC at T=50C

XG at T=30C

XG at T=40C

XG at T=50C

GG at T=30C

GG at T=40C

GG at T=50C

b


PAM and PEO. Since these polymers are flexible, it is probably expected that they are more

prone to mechanical degradation due to flow rate increment. The drag-reducing mechanism in

flexible polymers is very diverse compared to the rigid ones and it is associated with the

microstructure of molecules, based on Virk et al. report [43]. The contradictory results reported

by White and Mungal [44], and Peyghambarzadeh et al [36] reported that DR% increases with

increasing fluid flow rate.

Fig. 4. The variation of the DR% with volume flow rate at different concentrations at d=1/2 in


0

5

10

15

20

25

30

5 7 9 11

DR

%

Q (l/min)

d=1/2 in,T=30 C

PAA,C=100 ppm

PAA,C=200 ppm

PAA,C=360 ppm

PAM,C=10 ppm

PAM,C=100 ppm

PAM,C=200 ppm

PEO,C=10 ppm

PEO,C=100 ppm

PEO,C=200 ppm

a

-40

-30

-20

-10

0

10

20

30

40

50

5 7 9 11

DR

%

Q (l/min)

d=1/2in,T=30 C

CMC,C=50 ppm

CMC,C=100 ppm

CMC,C=200 ppm

GG,C=10 ppm

GG,C=250 ppm

GG,C=500 ppm

XG,C=100 ppm

XG,C=500 ppm

XG,C=1000 ppm

b


Fig. 5. The variation of the DR% with volume flow rate at various concentrations at d=3/4 in


The important roles of temperature contain the impact on polymer solubility in the fluid,

polymer degradation, and liquid viscosity. To assess the temperature impact, considering these

influences simultaneously is essential. With increasing temperature, the polymer molecules’

tendency to extending will increment. The higher temperature will result in more solubility of

the DRAs in water flow. The interactions within fluid and DRA involve two problems; one is

polymer particle agglomeration during cold flow probably leading to a reduction in polymer

solubility in the fluid. Thermal degradation is another problem that may impose damaging

impacts on the polymer chain and thereby the DRA performance. Therefore, the impacts of

0

10

20

30

40

50

60

5 6 7 8 9 10 11

DR

%

Q (l/min)

d=3/4 in,T=30 C

PAA,C=100 ppm

PAA,C=200 ppm

PAA,C=360 ppm

PAM,C=10 ppm

PAM,C=100 ppm

PAM,C=200 ppm

PEO,C=10 ppm

PEO,C=100 ppm

PEO,C=200 ppm

a

-65

-55

-45

-35

-25

-15

-5

5

15

25

5 6 7 8 9 10 11

DR

%

Q (l/min)

d=3/4in,T=30 C

GG,C=10 ppm

GG,C=250 ppm

GG,C=500 ppm

CMC,C=50 ppm

CMC,C=100 ppm

CMC,C=200 ppm

XG,C=100 ppm

XG,C=500 ppm

XG,C=1000 ppm

b


temperature on the drag-reducing phenomenon strongly rely on the utilized experimental

temperature range. Figs. 6a and 6b represent the change in DR% with the polymer concentration

and operating temperature at a constant flow rate of 6 l/min inside the ½ inches pipe. Results

show that the effect of temperature on the DR% is not uniform for different polymeric solutions.

As can be seen, increasing temperature enhances the DR% for PEO. It can be caused by the

lower viscosity of the working fluid at higher temperatures. Furthermore, higher temperatures

increase the DRA solubility in distilled water [45]. Probably, these two factors simultaneously

increase the influence of PEO at higher temperatures. The mentioned result is following [4, 22,

36]. On the other hand, DR% for PAA and XG decreases with increasing temperature. In this

regard, it was shown that the effect of temperature on the DR% for PAM and CMC is not

considerable. Previously, Interthal and Wilski [46] showed that increasing temperature from 5

to 35 oC did not change the DR%. They used partially hydrolyzed PAM at 30 ppm concentration

inside the 14 mm diameter pipe and the Re= 100’000. Nevertheless, it is not possible to

determine whether a similar temperature trend is true for all researchers since the published

studies are very limited in this regard. It can be understood that owing to the complexity of the

6 stated concepts in the DRA performance and flow, providing a firm conclusion is difficult

regarding the influence of temperature on DR%.

Fig. 6. The change in the DR% with concentration at various temperatures (d=1/2 in,

Q=6 l/min), (a) Synthetic DRA (b) Biological DRA

0

10

20

30

40

0 100 200 300 400

DR

%

C (ppm)

d=1/2 in,Q=6l/min

PAA,T=30C

PAA,T=40C

PAA,T=50C

PAM,T=30C

PAM,T=40C

PAM,T=50C

PEO,T=30C

PEO,T=40C

PEO,T=50C

a

-50

-40

-30

-20

-10

0

10

20

30

40

50

0 200 400 600 800 1000

DR

%

C (ppm)

d=1/2in,Q=6 l/min

CMC,T=30C

CMC,T=40C

CMC,T=50C

XG,T=30C

XG,C=40C

XG,T=50C

GG,C=30C

GG,C=40C

GG,T=50C

b


Table 4 shows the average values of DR% for different polymers at their best concentration

(which is the highest concentration) inside the ½ and ¾ inches pipes. As can be seen, all the

polymers enhanced the DR% except for GG that enhances the drag in the fluid flow with

average values of 35% and 61% for ½ and ¾ inches pipes, respectively. Also, results show that

DR% enhances with increasing the pipe diameter for the synthetic polymers of PAA, PAM, and

PEO, but this effect is not obvious for biological polymeric solutions like CMC and XG.

Though various researchers investigated the influence of pipe diameter on the efficiency of

DRP, the effect of variation in the internal diameter (ID) of the conduit or pipe on the quantity

of drag-reducing (DR%) is still controversial since the conclusion of researchers are not

consistent on this matter. Nevertheless, one of the most complete findings on the effect of DRPs

was provided by Interthal and Wilski [46] via factors like pipe diameter. They reported the

increase in drag-reducing from 66% at 3-mm ID to a peak of 80% at 14-mm ID and then the

reduction to 76% at the maximum 30-mm ID. This outcome approved the nonexistence of

persistence in the change in drag-reducing with pipe diameters. In another similar work

conducted by Karami and Mowla [4], the drag-reducing of 3 different various solutions was

investigated with a similar concentration of 200 ppm and at 29 ◦C in two rough galvanized iron

pipes with 0.0254 and 0.0127 m IDs. They found that the DR was reduced by increasing the

diameter of the pipe for all the polymer solutions.

Table 4. The effectiveness of the polymeric DRAs

%DRave d(in) %DRave d(in) C(ppm) DRA

31 ¾ 22 1/2 200 PEO

36 ¾ 18 1/2 200 PAM

26 ¾ 17 1/2 360 PAA

14 ¾ 16 1/2 200 CMC

21 ¾ 29 1/2 1000 XG

-61 ¾ -35 1/2 500 GG

Figs. 7a and 7b demonstrate the variation of Darcy friction factor against volume flow rate

at different concentrations for synthetic and biological polymers at 30 oC inside ½ and ¾ inches

pipes. Results show that except for the case of GG, distilled water has the greatest friction

factor. Furthermore, more decrease in the friction factor could be observed at higher

concentrations of the polymeric solution.

Drag reducing in Prandtl–Karman coordinates

Utilizing Prandtl–Karman coordinates, it is possible to compare the degree of DR of polymer

solutions regarding the drag-reducing boundaries; the start of drag-reducing as the departure

point from Prandtl–Karman law and maximum drag-reducing (MDR) or Virk’s asymptote [13,

44]. Fig. 8 demonstrates Prandtl-Karman coordinates for different polymers at all the

concentrations and constant temperature of 30 oC inside the ½ inches pipe. As can be seen, all

the experimental data alight among the Virk and Prandtl-Karman asymptotes. Distilled water

data showed about a 12% deviation from the Prandtl-Karman relation which is a confirmation

for calibration and accuracy of the apparatus. The experimental friction factor also showed the

same deviation as the Colebrook equation.

Results show that for the concentration range of this study, DR is lower than the maximum

DR predicted by Virk. So, it is expected that DR% enhances with increasing polymer

concentration. PAA and PEO polymeric solutions were approaching Virk maximum drag-

reducing relation. It is shown that these polymers have higher efficiency in drag-reducing. The

experimental data for GG had the most distance from Prandtl-Karman prediction which


indicates this polymer did not have drag-reducing property. Also, Results show that all the data

could be predicted with Prandtl–Karman equation with a deviation between -12 to 35 percent.

Fig. 7. The variation of the friction factor with volume flow rate at various concentrations at d=1/2 in (a)

Synthetic DRA (b) Biological DRA

It should be emphasized that contrary to some other researches [47, 48] that reported drag-

reducing polymers could reach the Virk relation, the results of the present study indicated that

the experimental data have a large deviation from Virk relation. The experimental data is well-

aligned with the Prandtl-Karman relation. Therefore, it was tried to forecast the polymers' drag-

reducing at the concentration range of this study using a modified Prandtl-Karman relation.

Results discovered that incrementing the polymer concentration enhances the slope of the line

0.02

0.024

0.028

0.032

0.036

5 7 9 11

f

Q (l/min)

d=1/2in,T=30C

PAA,C=100 ppm

PAA,C=200 ppm

PAA,C=360 ppm

PAM,C=10 ppm

PAM,C=100 ppm

PAM,C=200 ppm

PEO,C=10 ppm

PEO,C=100 ppm

PEO,C=200 ppm

Water

a

0.02

0.025

0.03

0.035

0.04

0.045

5 7 9 11

f

Q (l/min)

d=1/2in,T=30C

CMC,C=50 ppm

CMC,C=100 ppm

CMC,C=200 ppm

GG,C=10 ppm

GG,C=250 ppm

GG,C=500 ppm

XG,C=100 ppm

XG,C=500 ppm

XG,C=1000 ppm

Water

b


in Prandtl-Karman relation. For example, Fig. 9 demonstrates these lines for PAA according to

the Prandtl-Karman type relation. It is shown that enhancing the PAA concentration from 100

to 360 ppm increases the slope from 1.852 to 2.848.

Fig. 8. Prandtl–Karman coordinates for polymeric DRA

According to the literature [49], it was proposed that the slope increase regarding the

Prandtl–Karman law is proportionate to the square root of polymer concentration (√𝐶) with

aproportionality constant that is the representative of the polymer. In this study, strong

proportionality obtained for all the polymers to C itself rather than √𝐶. Table 5 indicates the

experimental data curve fitting for all the polymers in the turbulent flow regime at 30 oC inside

½ inches pipe. So, the values of A as the slope of the Prandtl–Karman law for each polymer

were obtained and reported in Table 5. Meanwhile, the modified presentations of Prandtl–

Karman law for each polymer are also shown in Table 5.

Fig. 9. Linear fit results for PAA (as an example for modification of Prandtl–Karman law)

5

7

9

11

13

15

0.2 0.7 1.2 1.7 2.2 2.7 3.2

f^-0

.5

log(Re.f^0.5)

T=30C,d=1/2 inPAA,C=100 ppm

PAA,C=200 ppm

PAA,C=360 ppm

PAM,C=10 ppm

PAM,C=100 ppm

PAM,C=200 ppm

PEO,C=10 ppm

PEO,C=100 ppm

PEO,C=200 ppm

CMC,C=50 ppm

CMC,C=100 ppm

CMC,C=200 ppm

XG,C=100 ppm

XG,C=500 ppm

XG,C=1000 ppm

GG,C=10 ppm

GG,C=250 ppm

GG,C=500 ppm

Water

P-K

Virk

+35%

-12%

y = 1.8524x + 5.6231

R² = 0.9999

y = 2.0957x + 5.6239

R² = 0.9999

y = 2.8489x + 5.6257

R² = 0.9998

0

2

4

6

8

10

12

14

0 1 2 3 4

f^-0

.5

log(Re.f^0.5)

PAA,C=100 ppm

PAA,C=200 ppm

PAA,C=360 ppm

Linear (PAA,C=100 ppm)




Table 5. Modification of Prandtl–Karman equation for polymeric DRA (T=30 °C, d=1/2 in)

DRA Linear fit equation A R2 Range of Conc (ppm)

PAA 1

√𝑓= 𝐴Log10(𝑅𝑒. √𝑓) + 5.62 0.003C+1.404 0.98 100-360

PAM 1

√𝑓= 𝐴𝐿𝑜𝑔10(𝑅𝑒. √𝑓) − 0.8 0.004C+3.754 0.97 10-200

PEO 1

√𝑓= 𝐴𝐿𝑜𝑔10(𝑅𝑒. √𝑓) + 5.56 0.001+1.91 0.97 10-200

CMC 1

√𝑓= 𝐴𝐿𝑜𝑔10(𝑅𝑒. √𝑓) + 4.5 0.003C+1.848 0.98 50-200

XG 1

√𝑓= 𝐴𝐿𝑜𝑔10(𝑅𝑒. √𝑓) + 3.14 0.001C+2.348 0.99 100-1000

GG 1

√𝑓= 𝐴𝐿𝑜𝑔10(𝑅𝑒. √𝑓) + 6.8 -0.0004C+1.222 0.94 10-500

Fig. 10 compares the prediction of obtained correlations with the experimental data in

Prandtl–Karman coordinates. The new correlations are in excellent agreement with the

empirical data. In this graph, the correlation developed by Habibpour et al [47] was also

presented. Habibpour et al [47] suggested a relation for the prediction of friction factor for

hydrolyzed PAM at the concentration of 100 and 200 ppm, respectively as follows:

1

√𝑓= 6 log10 𝑅𝑒 . √𝑓 − 4.1 (8)

1

√𝑓= 9.3 log10 𝑅𝑒 . √𝑓 − 7.3 (9)

It is clear from Fig. 10 that Eq. 8 for the concentration of 100 ppm is in better agreement

with the empirical data obtained in this study while the prediction of Eq. 9 for 200 ppm is not

acceptable. This may be due to the difference in polymer molecular weight, the extent of

hydrolyzing, and operating conditions.

Fig. 10. Comparison of the experimental values with the values obtained correlations [47] and present study

10

12

14

16

18

20

22

2.8 2.9 3 3.1 3.2 3.3

f^-0

.5

log (Re.f^0.5)

PAM,C=100 ppm(EXP)

PAM,C=200 ppm(EXP)

Habibpour Correlation,C=100 ppm

Habibpour Correlation,C=200 ppm

P-K

Present Correlation,C=100 ppm

Present Correlation,C=200 PPM

P-K


Conclusion

In this study, a large number of experimental data was gathered for drag-reducing properties

of almost all water-soluble polymers including PAA, PAM, CMC, GG, XG, and PEO for fluid

flow in turbulent regime inside the smooth circular pipes. Furthermore, the effects of different

parameters like polymer concentration, temperature, fluid flow rate, pipe diameter, and type of

polymer were rigorously studied. Due to a large number of operating factors and their levels of

variation, and considering the repeatability tests, more than 1000 experimental data were

obtained and analyzed.

The significant findings can be summarized as follows:

- The addition of all the polymers except for GG enhanced the DR%.

- GG deteriorated the drag-reducing up to 61%. It did not have drag-reducing property.

- DR% increases with increasing polymer concentration.

- Change of pipe diameter showed different effects on the drag-reducing for different

polymers. The efficiency of the drag-reducing improved for some of them like PEO,

PAM, and PAA in larger diameter pipe. This effect was not considered for biological

polymers like CMC and XG.

- The influence of temperature on the efficiency of the drag-reducing was not uniform for

all the polymers. Increasing the temperature enhances DR% for PEO while it reduces

DR% for PAA and XG. Indeed, the effect of temperature on PAM and CMC was not

obvious.

- The experimental data had a large deviation with Virk relation. They scattered in the

vicinity of the Prandtl-Karman relation with a deviation of less than 35%.

- A modified version of the Prandtl-Karman relation was proposed for each polymer

which could predict the experimental data with better accuracy.

- Considering the probability of polymer degradation according to fluid flow shear stress,

it is suggested that the drag-reducing properties of the polymers will be studied in the

future considering the degradation tendency of the polymers.

Nomenclature C Polymer concentration (ppm)

CMC Carboxymethyl cellulose

DR Drag reduction

DRAs Drag reducing agents

DRPs Drag reducing polymers

Exp Experimental

f Friction factor

GG Guar Gum

l Litter

L Tube Length (m)

P Pressure (Pa)

PID Proportional–integral–derivative

ppm Parts per million

PAA Polyacrylic acid

PAM Polyacrylamide

PEO Polyethylene oxide

OTEC Ocean thermal energy conversion

Q Volume flow rate (l/min)


Re Reynolds number

SDS Sodium dodecyl sulfate

T Temperature (°C)

�̅� Velocity (m/s)

XG Xanthan Gum

Greek symbols

ε Roughness (m)

μ Viscosity (Pa.s)

ρ Density (kg/m3)

δ Slope

Subscripts

p Polymeric solution

w Water (solvent)

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Experimental Investigation of Drag Reduction in Turbulent